Free Particle moving in one dimension problem

[EmmaKate2009]

Homework Statement

5) A free particle moving in one dimension is in the state

Ψ(x) = ∫ isin(ak)e^(−(ak)2/2)e^(ikx) dk

a) What values of momentum will not be found?
b) If the momentum of the particle in this state is measured, in which momentum
state is the particle most likely to be found?
c) if a=2.1 angstrom and the particle is an electron, what value of energy (in
eV) will measurement find in the state described in part b?

Homework Equations

I know tha p=ħk

The Attempt at a Solution

I have attempted to complete the integration but this seems to go into very confusing and very difficult terms. I'm thinking that there is something simpler and I am just missing it.

 

[DrClaude]

Do you know what that integral represents?

 

[EmmaKate2009]

Do you know what that integral represents?

the integral is from - infinity to + infinity, I just didn't know how to put it on the question on here

 

[DrClaude]

the integral is from - infinity to + infinity, I just didn't know how to put it on the question on here

I understand that.

My point is that the integral is a very specific kind. If you can figure out out what it is, you get the momentum representation of the wave function with no effort.

 

[EmmaKate2009]

I understand that.

My point is that the integral is a very specific kind. If you can figure out out what it is, you get the momentum representation of the wave function with no effort.

I'm not sure I understand your statement. I know that a wave function can be either classified as sines and cosines or as exponentials, I haven't yet seen a wave function that includes a integral before.

 

[DrClaude]

I'm not sure I understand your statement. I know that a wave function can be either classified as sines and cosines or as exponentials, I haven't yet seen a wave function that includes a integral before.

I'm surprised that you have such a problem to solve if you haven't seen such an integral before. It is a Fourier transform.